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All instances / J1-J2

J1-J2 square 16x16, J2 = 0.5

J1J2/square_256_P_0.5

Record

-0.4969140(5) E/N (S.S)

CNN-MPS

Fan et al. (2026) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑⟨ij⟩ σi·σj + J2⟨⟨ij⟩⟩ σi·σj

J1 = 1, J2 = 0.5, nearest and next-nearest neighbours, written with Pauli matrices.

lattice
square
sites
256
boundary
periodic
J2
0.5
energies
3

Stored as a total energy in the convention of VarBench; quoted here as E/N (S.S), which is what the papers report (how the conversion works).

Every published energy

Grouped by what the number is. Ranking happens only inside the first group.

Strict variational upper bounds (3)

The record is the lowest eligible energy in this group, and only this group.

E/N (S.S)σVar(E)V-score methodsourceyear
-0.4969140(5)record 5.0e-7 n/a n/a CNN-MPS
preprint
Fan et al. (2026) 2026
-0.496786(1) 1.0e-6 n/a n/a T-MPS
preprint
Fan et al. (2026) 2026
-0.4967163(8) 8.0e-7 n/a n/a ResNet2 (64 conv layers), MinSR
peer reviewed
Chen & Heyl (2023) 2023

How these numbers were read

Rows added after the VarBench import record where the number came from.

-0.4969140(5) — CNN-MPS

Checked 2026-09-13 · arXiv HTML parsed locally, no LLM transcription

Reported as. -0.496914 (+/- 5e-7) per site in S.S units

Read from Table 1 of arXiv:2603.14425 (square-lattice J1-J2 at J2/J1=0.5, PBC, E per site in S.S units), parsed from the arXiv HTML. Claim: "For L=16, CNN-MPS yields the lowest variational energy, -0.4969140(5), compared with the previously best reported value -0.4967163(8)".

-0.496786(1) — T-MPS

Checked 2026-09-13 · arXiv HTML parsed locally, no LLM transcription

Reported as. -0.496786 (+/- 0.000001) per site in S.S units

Read from Table 1 of arXiv:2603.14425 (square-lattice J1-J2 at J2/J1=0.5, PBC, E per site in S.S units), parsed from the arXiv HTML.

-0.4967163(8) — ResNet2 (64 conv layers), MinSR

Checked 2026-09-10 · source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription

Reported as. -0.4967163 (+/- 8e-7) per site in S.S units

PDF text: "our approach yields the best variational energy E/N = -0.4967163(8) ... on such a large lattice" (16x16). No VarBench instance existed for this size.

Coverage

Newest published number here: 2026. 3 rows added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

This instance as data

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